RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.69 22.5247 0.834628
2 to 25 15.64 14.2267 0.349008
3 to 26 15.74 14.8309 0.392339
4 to 27 15.87 23.1537 0.855686
5 to 28 15.82 12.7907 0.249920
6 to 29 15.49 17.6178 0.586674
7 to 30 15.75 19.3505 0.691213
8 to 31 15.80 16.8116 0.532803
9 to 32 15.44 21.0838 0.777434
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.471060
Tough bday spacings test for dh-ranFile-2018-06-15_23:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 10 44 64 90 106 71 53 34 16 8 4
(O-E)^2/E 0.1 1.5 1.2 0.6 0.7 0.7 0.0 0.6 0.1 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.688, p= 0.159
RESULTS OF GCD FOR dh-ranFile-2018-06-15_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.623012
p-value, dist. of gcd's: 0.474560
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.018 0.448 0.634 0.115 0.280 0.201 0.689 0.571
Bits 8 to 15---> 0.778 0.931 0.654 0.229 0.471 1.000 0.298 0.999
Bits 16 to 23---> 0.171 0.548 0.377 0.838 0.721 0.070 0.958 0.059
Bits 24 to 31---> 0.523 0.252 0.317 0.755 0.184 0.598 0.169 0.899
KS test for the above 32 p values: 0.327
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_23:31,
p-values for 5 runs: 0.5914, 0.3277, 0.4909, 0.2430, 0.8210
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5130 5134.0 0.003 0.638
r= 30 23162 23103.0 0.150 0.788
r= 31 11485 11551.5 0.383 1.171
chi-square = 1.171 with df = 3; p-value = 0.240
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5205 5134.0 0.982 1.120
r= 31 23232 23103.0 0.720 1.840
r= 32 11357 11551.5 3.276 5.116
chi-square = 5.116 with df = 3; p-value = 0.836
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_23:31
b-rank test for bits 1 to 8, p=0.20865
b-rank test for bits 2 to 9, p=0.57543
b-rank test for bits 3 to 10, p=0.59401
b-rank test for bits 4 to 11, p=0.84202
b-rank test for bits 5 to 12, p=0.78329
b-rank test for bits 6 to 13, p=0.29765
b-rank test for bits 7 to 14, p=0.76817
b-rank test for bits 8 to 15, p=0.97559
b-rank test for bits 9 to 16, p=0.93404
b-rank test for bits 10 to 17, p=0.71607
b-rank test for bits 11 to 18, p=0.39947
b-rank test for bits 12 to 19, p=0.92854
b-rank test for bits 13 to 20, p=0.72817
b-rank test for bits 14 to 21, p=0.14690
b-rank test for bits 15 to 22, p=0.42510
b-rank test for bits 16 to 23, p=0.69540
b-rank test for bits 17 to 24, p=0.10370
b-rank test for bits 18 to 25, p=0.09464
b-rank test for bits 19 to 26, p=0.82288
b-rank test for bits 20 to 27, p=0.90991
b-rank test for bits 21 to 28, p=0.37020
b-rank test for bits 22 to 29, p=0.88471
b-rank test for bits 23 to 30, p=0.44753
b-rank test for bits 24 to 31, p=0.14094
b-rank test for bits 25 to 32, p=0.02307
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.563537
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_23:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 141149 -1.78 0.037828
2 141180 -1.70 0.044187
3 142314 0.95 0.827796
4 141813 -0.23 0.410962
5 141681 -0.53 0.296850
6 141532 -0.88 0.188993
7 141898 -0.03 0.489440
8 142360 1.05 0.853822
9 142083 0.41 0.657545
10 142018 0.25 0.600214
11 141401 -1.19 0.117478
12 141720 -0.44 0.329114
13 142106 0.46 0.677066
14 141400 -1.19 0.117019
15 141736 -0.40 0.342747
16 141890 -0.05 0.481989
17 142038 0.30 0.618152
18 141250 -1.54 0.061720
19 141112 -1.86 0.031237
20 142668 1.77 0.961852
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_23:31
Bits used No. missing words z-score p-value
23 to 32 141693 -0.7460 0.227844
22 to 31 141878 -0.1080 0.456984
21 to 30 142152 0.8368 0.798646
20 to 29 141760 -0.5149 0.303301
19 to 28 142175 0.9161 0.820194
18 to 27 141525 -1.3253 0.092540
17 to 26 142138 0.7885 0.784803
16 to 25 141744 -0.5701 0.284304
15 to 24 141493 -1.4356 0.075555
14 to 23 141715 -0.6701 0.251396
13 to 22 142028 0.4092 0.658806
12 to 21 141590 -1.1011 0.135418
11 to 20 141787 -0.4218 0.336575
10 to 19 141658 -0.8667 0.193066
9 to 18 141646 -0.9080 0.181930
8 to 17 141873 -0.1253 0.450153
7 to 16 141829 -0.2770 0.390890
6 to 15 141361 -1.8908 0.029326
5 to 14 141799 -0.3804 0.351806
4 to 13 142029 0.4127 0.660070
3 to 12 142100 0.6575 0.744565
2 to 11 142272 1.2506 0.894457
1 to 10 142679 2.6540 0.996023
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_23:31
Bits used No. missing words z-score p-value
28 to 32 141766 -0.4859 0.313532
27 to 31 142179 0.9141 0.819677
26 to 30 142022 0.3819 0.648744
25 to 29 141964 0.1853 0.573512
24 to 28 141749 -0.5435 0.293396
23 to 27 142518 2.0633 0.980457
22 to 26 141867 -0.1435 0.442951
21 to 25 142082 0.5853 0.720834
20 to 24 141523 -1.3096 0.095167
19 to 23 141265 -2.1842 0.014475
18 to 22 142285 1.2735 0.898572
17 to 21 142212 1.0260 0.847554
16 to 20 141514 -1.3401 0.090106
15 to 19 141503 -1.3774 0.084196
14 to 18 141982 0.2463 0.597290
13 to 17 142269 1.2192 0.888620
12 to 16 141961 0.1752 0.569520
11 to 15 141663 -0.8350 0.201854
10 to 14 142435 1.7819 0.962620
9 to 13 141702 -0.7028 0.241086
8 to 12 141788 -0.4113 0.340431
7 to 11 142019 0.3718 0.644965
6 to 10 141845 -0.2181 0.413688
5 to 9 142059 0.5074 0.694048
4 to 8 142055 0.4938 0.689275
3 to 7 141908 -0.0045 0.498201
2 to 6 142326 1.4124 0.921090
1 to 5 142065 0.5277 0.701145
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_23:31
Bits used No. missing words z-score p-value
31 to 32 141911 0.0049 0.501965
30 to 31 141890 -0.0570 0.477264
29 to 30 141733 -0.5201 0.301480
28 to 29 141802 -0.3166 0.375771
27 to 28 141911 0.0049 0.501965
26 to 27 141822 -0.2576 0.398354
25 to 26 142099 0.5595 0.712089
24 to 25 142160 0.7394 0.770180
23 to 24 141669 -0.7089 0.239182
22 to 23 141914 0.0138 0.505496
21 to 22 141704 -0.6057 0.272359
20 to 21 142463 1.6332 0.948791
19 to 20 141862 -0.1396 0.444482
18 to 19 142099 0.5595 0.712089
17 to 18 142148 0.7040 0.759297
16 to 17 142558 1.9135 0.972157
15 to 16 142564 1.9312 0.973270
14 to 15 141707 -0.5968 0.275306
13 to 14 142268 1.0580 0.854978
12 to 13 141793 -0.3432 0.365740
11 to 12 141906 -0.0098 0.496081
10 to 11 141814 -0.2812 0.389275
9 to 10 141277 -1.8653 0.031071
8 to 9 142024 0.3383 0.632416
7 to 8 141717 -0.5673 0.285240
6 to 7 141976 0.1967 0.577956
5 to 6 141734 -0.5172 0.302509
4 to 5 141806 -0.3048 0.380256
3 to 4 141935 0.0757 0.530180
2 to 3 141912 0.0079 0.503142
1 to 2 141830 -0.2340 0.407488
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2368.71 -1.857 0.031672
Test results for specific bytes for dh-ranFile-2018-06-15_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2494.38 -0.080 0.468314
2 to 9 2519.30 0.273 0.607535
3 to 10 2508.90 0.126 0.550095
4 to 11 2434.05 -0.933 0.175486
5 to 12 2488.64 -0.161 0.436182
6 to 13 2597.15 1.374 0.915275
7 to 14 2695.54 2.765 0.997156
8 to 15 2289.90 -2.971 0.001483
9 to 16 2523.26 0.329 0.628892
10 to 17 2447.36 -0.744 0.228317
11 to 18 2527.16 0.384 0.649572
12 to 19 2507.13 0.101 0.540151
13 to 20 2438.13 -0.875 0.190790
14 to 21 2465.43 -0.489 0.312435
15 to 22 2534.42 0.487 0.686773
16 to 23 2481.23 -0.265 0.395358
17 to 24 2444.81 -0.781 0.217527
18 to 25 2589.52 1.266 0.897250
19 to 26 2484.77 -0.215 0.414729
20 to 27 2515.66 0.221 0.587609
21 to 28 2633.11 1.882 0.970113
22 to 29 2467.72 -0.456 0.324018
23 to 30 2545.04 0.637 0.737920
24 to 31 2567.03 0.948 0.828408
25 to 32 2414.88 -1.204 0.114325
CDPARK for dh-ranFile-2018-06-15_23:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3537 0.6393 0.738676
3544 0.9589 0.831196
3510 -0.5936 0.276387
3499 -1.0959 0.136563
3544 0.9589 0.831196
3518 -0.2283 0.409702
3497 -1.1872 0.117571
3488 -1.5982 0.055002
3537 0.6393 0.738676
3533 0.4566 0.676028
Square side=100, avg. no. parked=3520.70 sample std.=19.98
p-value of the KSTEST for those 10 p-values: 0.795471
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_23:31
0.1857,0.9201,0.3926,0.4094,0.7519,0.9793,0.4528,0.8537,0.5923,0.1926,
The KS test for those 10 p-values: 0.673346
The 3DSPHERES test for dh-ranFile-2018-06-15_23:31
sample no r^3 equiv. uni.
1 41.439 0.748750
2 19.465 0.477337
3 12.421 0.339011
4 0.622 0.020533
5 15.208 0.397661
6 11.877 0.326930
7 79.590 0.929561
8 8.262 0.240730
9 33.126 0.668519
10 18.099 0.453003
11 27.968 0.606337
12 32.916 0.666192
13 28.110 0.608194
14 62.255 0.874463
15 85.776 0.942685
16 41.062 0.745573
17 12.991 0.351469
18 58.422 0.857355
19 39.588 0.732757
20 10.627 0.298277
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.435214
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 0.3 -0.1 -0.2 0.2
0.3 -0.0 -0.5 0.2 -1.2 -1.7
0.1 -0.1 0.5 1.3 0.6 1.6
-0.6 0.9 -0.7 -1.8 -0.9 0.6
0.6 -0.5 -0.4 -1.5 0.1 1.3
-0.2 1.3 -0.7 1.5 1.7 1.1
-0.5 -0.1 0.1 -1.3 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:34.699044
z-score=-0.796600, p-value=0.219418
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_23:31
Test no p-value
1 0.008652
2 0.041999
3 0.741884
4 0.839327
5 0.543543
6 0.413582
7 0.627327
8 0.009516
9 0.076463
10 0.900396
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.102307
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_23:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66769 0.16 66694 0.01
3 25000.00 24996 0.00 25056 0.13
4 6666.67 6620 0.33 6701 0.18
5 1388.89 1356 0.78 1306 4.95
6 238.10 215 2.24 206 4.33
7 34.72 37 0.15 30 0.64
8 4.96 6 0.22 6 0.22
p=0.30591 p=0.89294
Number of rngs required: 688053, p-value: 0.343
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_23:31
No. of wins: Observed Expected
98656 98585.9
z-score= 0.314, pvalue=0.62313
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66632 66666.7 0.018 0.018
2 37854 37654.3 1.059 1.077
3 26763 26954.7 1.364 2.441
4 19319 19313.5 0.002 2.442
5 13817 13851.4 0.086 2.528
6 10059 9943.5 1.341 3.868
7 7119 7145.0 0.095 3.963
8 5134 5139.1 0.005 3.968
9 3756 3699.9 0.852 4.820
10 2686 2666.3 0.146 4.966
11 1894 1923.3 0.447 5.413
12 1343 1388.7 1.507 6.919
13 975 1003.7 0.822 7.741
14 682 726.1 2.683 10.424
15 530 525.8 0.033 10.457
16 410 381.2 2.184 12.641
17 251 276.5 2.359 14.999
18 209 200.8 0.332 15.332
19 153 146.0 0.337 15.669
20 102 106.2 0.167 15.836
21 312 287.1 2.157 17.993
Chisq= 17.99 for 20 degrees of freedom, p= 0.41214
SUMMARY of craptest
p-value for no. of wins: 0.623131
p-value for throws/game: 0.412140
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_23:31
No. of wins: Observed Expected
98645 98585.9
z-score= 0.265, pvalue=0.60431
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66769 66666.7 0.157 0.157
2 37756 37654.3 0.275 0.432
3 26617 26954.7 4.232 4.663
4 19388 19313.5 0.288 4.951
5 13807 13851.4 0.142 5.093
6 9954 9943.5 0.011 5.104
7 7308 7145.0 3.717 8.822
8 5184 5139.1 0.393 9.215
9 3707 3699.9 0.014 9.228
10 2566 2666.3 3.773 13.001
11 1921 1923.3 0.003 13.004
12 1410 1388.7 0.325 13.329
13 956 1003.7 2.268 15.598
14 727 726.1 0.001 15.599
15 508 525.8 0.605 16.204
16 421 381.2 4.166 20.370
17 286 276.5 0.324 20.694
18 186 200.8 1.095 21.789
19 125 146.0 3.016 24.805
20 105 106.2 0.014 24.819
21 299 287.1 0.492 25.311
Chisq= 25.31 for 20 degrees of freedom, p= 0.81021
SUMMARY of craptest
p-value for no. of wins: 0.604308
p-value for throws/game: 0.810212
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0015,0.0087,0.0095,0.0145,0.0177,0.0205,0.0231,0.0293,0.0311,0.0312,
0.0317,0.0378,0.0420,0.0442,0.0550,0.0590,0.0617,0.0696,0.0756,0.0765,
0.0842,0.0901,0.0925,0.0946,0.0952,0.1023,0.1037,0.1143,0.1153,0.1170,
0.1175,0.1176,0.1354,0.1366,0.1409,0.1469,0.1592,0.1689,0.1713,0.1755,
0.1819,0.1837,0.1857,0.1890,0.1908,0.1926,0.1931,0.2012,0.2019,0.2086,
0.2175,0.2194,0.2278,0.2283,0.2286,0.2392,0.2401,0.2407,0.2411,0.2430,
0.2499,0.2514,0.2515,0.2724,0.2753,0.2764,0.2803,0.2843,0.2852,0.2934,
0.2969,0.2976,0.2977,0.2983,0.3015,0.3025,0.3033,0.3059,0.3124,0.3135,
0.3172,0.3240,0.3269,0.3273,0.3277,0.3291,0.3366,0.3390,0.3404,0.3427,
0.3434,0.3490,0.3515,0.3518,0.3657,0.3702,0.3758,0.3769,0.3803,0.3893,
0.3909,0.3923,0.3926,0.3954,0.3977,0.3984,0.3995,0.4075,0.4094,0.4097,
0.4110,0.4121,0.4136,0.4137,0.4147,0.4251,0.4352,0.4362,0.4430,0.4445,
0.4475,0.4478,0.4502,0.4528,0.4530,0.4570,0.4683,0.4711,0.4714,0.4746,
0.4773,0.4773,0.4820,0.4894,0.4909,0.4961,0.4982,0.5020,0.5020,0.5031,
0.5055,0.5231,0.5302,0.5328,0.5402,0.5435,0.5479,0.5501,0.5635,0.5695,
0.5706,0.5735,0.5754,0.5780,0.5867,0.5876,0.5914,0.5923,0.5940,0.5973,
0.5980,0.6002,0.6043,0.6063,0.6075,0.6082,0.6182,0.6230,0.6231,0.6273,
0.6289,0.6324,0.6341,0.6450,0.6487,0.6496,0.6538,0.6575,0.6588,0.6601,
0.6662,0.6685,0.6733,0.6760,0.6771,0.6868,0.6891,0.6893,0.6912,0.6940,
0.6954,0.7011,0.7121,0.7121,0.7161,0.7207,0.7208,0.7282,0.7328,0.7379,
0.7387,0.7387,0.7419,0.7446,0.7456,0.7487,0.7519,0.7546,0.7593,0.7682,
0.7702,0.7774,0.7781,0.7833,0.7848,0.7955,0.7986,0.8102,0.8197,0.8202,
0.8210,0.8229,0.8278,0.8284,0.8312,0.8312,0.8346,0.8365,0.8377,0.8393,
0.8420,0.8476,0.8537,0.8538,0.8550,0.8557,0.8574,0.8745,0.8847,0.8886,
0.8929,0.8945,0.8973,0.8986,0.8992,0.9004,0.9099,0.9153,0.9201,0.9211,
0.9285,0.9296,0.9307,0.9340,0.9427,0.9488,0.9581,0.9619,0.9626,0.9701,
0.9722,0.9733,0.9756,0.9793,0.9805,0.9960,0.9972,0.9991,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.903041
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.